Remember, it's impossible to actually counter a spell with counterspell, because if you are in range to counter them then they are necessarily in range to counter you. Instead, the point of counterspell is to make them waste their reaction, so they can't use shield that round.
It's totally possible. Only wizards, sorcerers, and warlocks have Counterspell on their spell list (and possibly high level Eldritch Knight or Arcane Trickster or Bard who took it with spell secrets). You can shut down a cleric, druid, or possibly a bard.
Plus a lot of monsters have innate spellcasting - and those can be counterspelled.
The other situation is having two or more spellcasters on your side with Counterspell. The enemy may counterspell your counterspell, but your buddy can in turn counterspell their counterspell.
Also, doing something to make them unable to see you makes you impossible to counterspell. (I love Staff of Swarming Insects for this reason - putting up the insect swarm isn't a spell, so can't be countered, and you can counterspell them unopposed after that.) Or be a sorcerer with Subtle spell.
In a game where arcane casters are common, counterspell tactics and strategies become highly imporant. In a game where enemy spellcasters are relatively rare...it's almost a wasted spell slot.